The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than per- mitting the olives to grow on their own and results in a smaller size olive. It also permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the nor- mal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Be- cause of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the maximum possible profit. (b) the best combination of barrels of pruned and regular olives. (c) the number of acres that the olive grower should devote to each growing process.

The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than per- mitting the olives to grow on their own and results in a smaller size olive. It also permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the nor- mal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Be- cause of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the maximum possible profit. (b) the best combination of barrels of pruned and regular olives. (c) the number of acres that the olive grower should devote to each growing process.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.4: Marketing Models

Problem 35P

See similar textbooks

Similar questions

Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than permitting the olives to grow on their own and results in a smaller size olive. It also, though, permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the normal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the…
Laredo Leather Company’s production manager, Jack Murray, has been under pressure from the company president to reduce the cost of conversion. In spite of several attempts to reduce conversion costs, they have remained more or less constant. Now Murray is faced with an upcoming meeting with the company president, at which he will have to explain why he has failed to reduce conversion costs. Murray has approached his friend, Jeff Daley, who is the corporate controller, with the following request: “Jeff, I’m under pressure to reduce costs in the production process. There is no way to reduce material cost, so I’ve got to get the conversion costs down. If I can show just a little progress in next week’s meeting with the president, then I can buy a little time to try some other cost-cutting measures I’ve been considering. I want you to do me a favor. If we raise the estimate of the percentage of completion of October’s inventory to 60 percent, that will increase the number of equivalent…
The seasonal yield of olives greatly increases by a process of branch pruning instead of olives by normal process. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the normal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. A barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. The best combination of barrels of pruned and regular olives in order to earn maximum profit X1(barrels of pruned) and X2( barrels of regular olives) One of the constraints of the problem is Select one: 2X1+5X2<=250 30X1+20X2<=250 2X1+2X2<=250 5X1+2X2<=250 5X1+2X2>=250
An entrepreneur is starting up a new bakery featuring a special pastry from an old family recipe. The basic dough recipe requires 5cups of flour, which is 0.75kg, plus another 0.75kg consisting of all the other ingredients, sugar, butter, milk, yeast, fruits, nuts and spices, to make the dough for 15 medium pastries. She runs some tests to scale up her recipe. In her first test batch she creates dough for 300 pastries, how much flour, in kg, was required?
The ore of a gold mine in the province contains, on average, 0,5 ounce of gold per ton Method A of processing costs 150Photon and recovers 93% of the gold, while Method B costs only 120Php/ton and recovers 81% of the gold. If gold can be sold at 1,200/ounce, which method is better and by how much?
A department works one 8-hour shift, 250 days a year, and has these figures for usage of amachine that is currently being considered:ProductAnnualDemandStandard ProcessingTime per Unit (hr)Processing TimeNeeded (hr)1 400 5.0 2,0002 300 8.0 2,4003 700 2.0 1,4005,800Units of capacity needed = Processing time needed ___________________________ Processing time capacity per unit (5–3)Working one 8-hour shift 250 days a year provides an annual capacity of 8 × 250 =2,000 hours per year. Consequently, three of these machines would be needed to handle therequired volume:5,800 hours __________________ 2,000
The Noname Computer Company builds a computer-designated model ICU2. It imports the motherboard of the computer from Taiwan, but the company inserts the sockets for the chips and boards in its plant in Lubbock, Texas. Each computer requires a total of ninety 64K dynamic random access memory (DRAM) chips. Noname sells the computers with three add-in boards and two disk drives. The company purchases both the DRAM chips and the disk drives from an outside supplier. Suppose that the forecasted demands for the computer for weeks 6 to 11 are 220, 165, 180, 180, 175, and 250. The starting inventory of assembled computers in week 6 will be 75, and the production manager anticipates returns of 30 in week 8 and 10 in week 10. The product structure diagram for the ICU2 computer is given in Figure below. a. Determine the MPS for the computers. b. Determine the planned order release for the motherboards assuming a lot-for lot scheduling rule. c. Determine the schedule of outside orders for the…
Joe is selling Christmas trees to pay his college tuition.He purchases trees for $10 each and sells them for $25each. The number of trees he can sell is normally distributedwith a mean of 100 and standard deviation of 30. How manytrees should Joe purchase?
Kpogas produces chairs and tables. Using economic forecast for the next month, Kpogas’ marketing manager has judged that during that period, it will be possible to sell as many chairs or tables as the company can produce. Management must now recommend a production target for next month. That is, how many chairs and tables should be produced if Kpogas’ management wishes to maximize next month’s profit contribution? Making this decision requires a consideration of the following key factors: ● Kpogas’s unit contribution margin is GH¢ 5,000 on each chair that is sold and GH¢ 4,000 on each table that is sold. ● Each product is put through Kpogas’s machining operations in both department A and department B. For next month’s production, the two departments have 150 and 160 hours available time, respectively. Each chair produced uses 10 hours of machining in department A and 20 hours of machining in department B, whereas each table produced uses 15 hours of machining in department A and 10…
A well-known multi-brand manufacturer uses the production lot sizing (EPQ) model to determine the production quantities of its various products. Product ABC is currently being produced in production batches of 5000 units. The production cycle length for this quantity is 10 days. Due to a recent shortage of raw material, the supplier announced that it will increase its prices. Current estimates are that the new raw material price will increase the cost of manufacturing the company's products by 28% per unit. What will be the new batch size after this price increase on the production batch size for ABC?